Question

A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio, and sells them at ₹192 per kg. 
The cost of variety P is ₹800 for 5 kg. 
The cost of variety Q is ₹800 for 4 kg. 
If the person gets an 8% profit, what is the P : Q ratio (by weight)? 

• A. 5 : 4
• B. 3 : 4
• C. 3 : 2
• D. 1 : 1

Hint:

In mixture problems involving profit, use assumed weights based on cost data to match the required profit percentage. Compare cost price and selling price for total quantity.

Answer 1

The Correct Option is A

Given:

\[ \text{Cost of 5 kg of variety P} = ₹800 \Rightarrow \text{Cost per kg} = ₹160 \] \[ \text{Cost of 4 kg of variety Q} = ₹800 \Rightarrow \text{Cost per kg} = ₹200 \]
Let the seller mix 5 kg of P and 4 kg of Q (to match the quantity from the cost data).

\[ \text{Total cost} = ₹800 + ₹800 = ₹1600 \] \[ \text{Total weight} = 5 + 4 = 9 \text{ kg} \] \[ \text{Selling price per kg} = ₹192 \Rightarrow \text{Total selling price} = 9 \times 192 = ₹1728 \]
\[ \text{Profit} = ₹1728 - ₹1600 = ₹128 \] \[ \text{Profit \%} = \frac{128}{1600} \times 100 = 8\% \]
Thus, the assumed mixture gives exactly 8% profit, which matches the condition. Therefore, the weight ratio P : Q is:

\[ 5 : 4 \]